In field emission an intense electric field, typically 5 to 10 V/nm, is applied to the surface of an electrically conductive material such as a refractory metal or semiconductor to lower the potential barrier so that electrons can tunnel into the surrounding medium such as air or vacuum. Theoretical studies suggest that the high density of conduction band electrons in metals could support field emission current densities as high as 1016 A/m2 [1]. However, the current density is usually much less than this limit because of instabilities that are caused by heating. Current densities that are near this limit are obtained when the electric field is applied in nanosecond pulses with a low duty cycle to limit the average heating. Currents as high as 20 to 40 mA [2] with current densities as high as 1015 A/m2 [1] are obtained from emitters smaller than 4 nm because this is much less than the mean free path for electron-phonon scattering (≈10 nm), which reduces the heating. Cooling a field emitter to temperatures of 2 to 4° K makes it possible to use currents that are two or three times those at room temperature [1]. By contrast, field emission tips of refractory metals such as tungsten with a radius of approximately 100 nm have an upper limit of 109 A/m2 in sustained operation at room temperature [3].
The maximum current that can be obtained by field emission does not increase in proportion to the area of the emitter. This may be understood because field emission is not uniform over the tip, but is limited to a small number of sites where contaminants reduce the work function or nanoprotrusions enhance the local electric field [4-7]. We have studied the large data base for field emitters of diamond having areas from 6×10−16 to 2×10−4 m2 to obtain the empirical equation I=5.5×A0.25, where I is the emitted current in milliamperes and A is the area of the emitter in square meters. Others have shown that the emitted current is proportional to A0.28 for copper and A0.24 for stainless steel [6]. Thus, increasing the field emission current from 1 μA to 1 mA would require that the area be increased by a factor of 1012 which is 109 times what would be necessary if the current density were independent of the area of the emitter.
Field emitter arrays (FEAs), having a large number of microtriodes with conical field emitters, are used to obtain a constant current density over large areas; e.g. 160 mA with an area of 7450 μm2 [10]. The total current can be stabilized by placing a single ballast resistor [11] or a single electronic constant-current source in series with the array [12]. It would not be practical to use either of these methods to divide the current evenly between all of the emitters in an array because the fabrication already requires multiple processes of deposition and lithography. However, FEAs have been made in which each emitter is formed on a separate pillar-shaped ungated field-effect transistor which limits the current for that emitter by velocity saturation [13]. Analyses of the effects of the structural parameters for FEAs, including the gate electrodes of the triodes and the small fraction of the total area contributing to the current, show that the overall current density from a FEA can not exceed 2.2×107 A/m2 for steady-state operation in vacuum [14], and FEAs that approach this limit have been demonstrated [10,15]. Field emitter arrays are the only example of prior art that can provide this high of an overall current density in steady-state over areas that are greater than 10 μm2.
This disclosure describes methods for increasing the total current of emitted electrons by increasing the effective area of a cathode instead of having a limited number of emitter sites. Such an increase in the current would be useful in many applications. For example, the output power could be increased in microwave and terahertz sources that are based on photomixing in laser-assisted field emission because the power is proportional to the square of the current but the size of the emitter must be less than the wavelength of the laser radiation [8]. The present invention is especially appropriate for applications where metal-insulator-metal (MIM) diodes are now used, such as high-speed mixers, in which the current is caused by electrons tunneling through a dielectric [9]. This is because the present invention uses a gas such as air or a vacuum in place of the solid dielectric so the dielectric constant is reduced to unity, and the current is caused by field emission so the gap may be much greater in length. These two changes cause the shunting capacitance, which limits high-frequency operation, to be much less than it is in MIM diodes. Thus, the present invention may be used at higher frequencies, or the cross-sectional area may be increased to provide much greater current. Other possible applications include gas ionizers, gas pressure sensors, and various types of microwave devices.